$f(x) = \dfrac{ x + 4 }{ ( x + 4 )( x - 7 ) }$ What is the domain of the real-valued function $f(x)$ ?
$f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-4$ or $x=7$ So we know that $x \neq -4$ and $x \neq 7$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-4, \,x \neq7\, \}$.